The study of human cardiomyopathies and the development and testing of new therapies has long been limited by the availability of appropriate in vitro model systems. Cardiomyocytes are highly specialized cells whose internal structure and contractile function are sensitive to the local microenvironment and the combination of mechanical and biochemical cues they receive. The complementary technologies of human induced pluripotent stem cell (hiPSC) derived cardiomyocytes (CMs) and microphysiological systems (MPS) allow for precise control of the genetics and microenvironment of human cells in in vitro contexts. These combined systems also enable quantitative measurement of mechanical function and intracellular organization. This review describes relevant factors in the myocardium microenvironment that affect CM structure and mechanical function and demonstrates the application of several engineered microphysiological systems for studying development, disease, and drug discovery.